相关论文: Towards a 2-dimensional notion of holonomy

We upgrade the classical operation of \textit{isomonodromic deformations} along a path $\gamma$ to a functor $\mathbb{P}_{\gamma}$ between categories of flat connections with logarithmic singularities along a divisor $D$, which itself…

We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…

We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of…

Holonomy invariants in strict higher gauge theory have been studied in depth, aiming to applications to higher Chern-Simons theory. For a flat 2-connection, the holonomy of surface knots of arbitrary genus has been defined and its…

We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two. These foliations produce local complex-valued harmonic…

Given a foliation, there is a well-known notion of holonomy, which can be understood as an action that differentiates to the Bott connection on the normal bundle. We present an analogous notion for Lie subalgebroids, consisting of an…

We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstructions to the existence of such connections, and we prove…

We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra from finitely presented, commutator-relators groups to arbitrary finitely presented groups. In the process, we give an explicit formula for…

In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Consequently, we use this cohomology to characterize…

The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…

For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic…

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation…

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we…

A bi-invariant differential 2-form on a Lie group G is a highly constrained object, being determined by purely linear data: an Ad-invariant alternating bilinear form on the Lie algebra of G. On a compact connected Lie group these have an…

We define and study the notion of a crossed module over an inverse semigroup and the corresponding $4$-term exact sequences, called crossed module extensions. For a crossed module $A$ over an $F$-inverse monoid $T$, we show that equivalence…

Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the "virtual structure" of its orbit space, the…

We study the notion of the Lie-holomorph of a Leibniz algebra, recently introduced by N. P. Souris as a generalisation of the classical holomorph construction for Lie algebras. We establish a connection between the Lie-holomorph…

We construct a cycle in higher Hochschild homology associated to the 2-dimensional torus which represents 2-holonomy of a non-abelian gerbe in the same way the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary…

We show how to integrate a weak morphism of Lie algebra crossed-modules to a weak morphism of Lie 2-groups. To do so we develop a theory of butterflies for 2-term L_infty algebras. In particular, we obtain a new description of the…